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Stores are racing to replenish depleted shelves and to calm shoppers anxiously preparing for coronavirus disruptions, but they are having trouble meeting the heightened demand.

"Hand sanitizer is going to be very difficult to have 100 percent on stock on for some time," Walmart CEO Doug McMillon said at a White House news conference Friday. "We're still replenishing it and shipping it, but as soon as it hits the stores, it's going."

McMillon said a stressed supply chain was responsible for the racks bare of paper products, water and cleaning supplies.

"All the retailers have been working hand in hand with the suppliers to bring that to the markets as fast as we can," he said.

Retailers are rerouting supplies to areas of the country that need it most. To prevent hoarding, they're applying or giving store managers power to set limits on the number of specific items a customer can buy in a single trip.

"As always, our focus is to have merchandise available for our members at low warehouse prices," a Costco spokesperson told NBC News.

In a statement, Target said its team is "working around the clock to make sure that the products you want are available when you need them."

"As demand for cleaning products, medicine, pantry stock-up items and more remains high, we're sending more products to our stores as quickly as possible," it said.

Some stores said they'd been preparing for the possibility that the outbreak could lead to more buying and were poised to switch to additional supply options and modified operations.

Mabrie G. Jackson, director of public affairs for the Texas supermarket chain H-E-B, tweeted that the retailer "has been preparing for coronavirus for several months and we are in a strong position to keep replenishing our shelves. Customers should not panic, we have the ability to restock shelves and encourage our customers to remain calm." The company also announced that it was temporarily reducing its store hours at most locations.

The pace of restocking and knowing whether supplies will last long depend on customer behavior and how much inventory each store's wholesaler or supplier has in the pipeline, said Joe Walsh, a retail grocery consultant.

"It's a store-by-store case, but for a majority of chains and independents, they will replenish from their wholesaler immediately," he said. "Every case of bath tissue currently produced in pipeline, at a wholesaler or a warehouse, all those are spoken for."

The real crunch is not the next shipment to restock after this week's panic buying but the one that comes after, Walsh said.

"They all have to buy from the same five to six places," he said, referring to the manufacturers. "We're going to see limits, allocations, restrictions." While stores might be able to slightly increase their usual order, they'll be limited by how much. "If they get five cases a week of Charmin, they might be able to buy 10," said Walsh.

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Customers should brace for the possibility of long lines, limits on the number of items they can buy, the disappearance of discounts for high-demand items and the possibility of price increases, Walsh said. And if stores cut hours excessively or if hourly employees like shelf stockers or cashiers self-quarantine and don't show up for work, lines could grow.

Logistics experts said they expect that stores will quickly figure out how to cope with the surprise spike in purchasing.

"The real reason for things running out is this 'run'" by shoppers, said Ananth Iyer, a professor of operations management at Purdue University. "They believe they need more of it and are not sure if it will be available when they want it. Retailers, given demand, will find a way to generate supply."

But smaller stores in particular may have to pay more if they want to get resupplied sooner. Stores could try to persuade shoppers to take smaller orders now and sign up for the rest next week or to sign up for weekly delivery and get more shoppers to buy groceries online, Iyer said.